Is there a way to pause animated GIF file, when movie is paused.
Is there a way to show/hide an image using Standard player Play/pause button??
If you mean the default buttons on a playbar, the answer is again negative. They are like buttons for a VCR or other player, no control by the developer.
If you want to do that, use custom navigation and buttons. Have a look at this interactive movie:
That one was meant to have the button timed for the rest of the project. If you have an individual instance on a slide you can edit the action to add the hide/show possiblitiy for an object or a group.